At peak strengths, the Union army had about 700,000 troops and one of the most powerful navies in the world. The Confederacy has a peak of about 350,000 troops. With the advent of the rifle, attacking forces required more men than dug in defenders. A foreign army would of had to ship hundreds of thousands of men to America to tip the scales. Logistically and in man power, it just couldn’t happen.
More realistically, there was always a threat of foreign support of the Confederacy so that they could become and independent country. After Gettysburg and Vicksburg, England and France stopped entertaining that idea.